Do Xbox Live Arcade games ever reduce in price, if they are older or during special sale events? I know Gold members get a deal-of-the-week but am unaware of anything beyond that.
Yes, sometimes they go on sale, or the creator can decide to change the price. During the summer, there are summer savings, and sometimes other ones too. It just varies.
Sometimes after a year or so there will be a permanent price drop, but there's no guarantee. And there are special deals every now and then, but you can't really predict what they will be. I keep track of this by subscribing to Joystiq's "Now Playing" RSS feed: http://www.joystiq.com/tag/now-playing/rss.xml
Every Tuesday they list the new releases for all consoles, including XBLA games and XBLA price changes. It's nice because I only have to look at it once a week. I'm sure there are other sites with similar content; Joystiq's just the one I'm familiar with.
You might also want to check out http://www.cheapassgamer.com, though I found it took a much bigger commitment to keep up with it.